0,1

Number of meaningful differential operations of the k-th order on the space R^3. - Branko Malesevic (malesevic(AT)kiklop.etf.bg.ac.yu), Feb 29 2004

Arxiv paper of 2007 generalizes Malesevic reference of 1998, giving recurrence relations through dimension 10, for which case f(i+6) = 5f(i+4) - 6f(i+2) + f(i). - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 07 2007

B. Malesevic: Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.

B. Malesevic: Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n

Branko Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, Apr 05 2007.

a(n) = Fib(n+4). a(n) = a(n-1) + a(n-2).

a(n)=A020695(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 28 2008

G.f.: (3+2x)/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]

Meaningful second-order differential operations appear in the form of five compositions as follows: 1. div grad f 2. curl curl F 3. grad div F 4. div curl F (=0) 5. curl grad f (=0)

Meaningful third-order differential operations appear in the form of eight compositions as follows: 1. grad div grad f 2. curl curl curl F 3. div grad div F 4. div curl curl F (=0) 5. div curl grad f (=0) 6. curl curl grad f (=0) 7. curl grad div F (=0) 8. grad div curl F (=0)

Subsequence of A000045, A020695. See A008776 for definitions of Pisot sequences.

Cf. A039834, A020695, A071679.

Sequence in context: A080614 A079122 A071679 this_sequence A024885 A133605 A131354

Adjacent sequences: A020698 A020699 A020700 this_sequence A020702 A020703 A020704

nonn

David W. Wilson (davidwwilson(AT)comcast.net)